Subgroups — C₃×#21439680 #37525035

Order 22932.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16838449	C₂	1	1	yes	maximal, characteristic
2	C₃×#14579331	C₃	1	1	yes	maximal, characteristic, complemented
3	#21439680	C₃	1	3	yes	maximal, direct product factor
4	C₃×#14274262	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₃×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic
6	#16838449	C₂×C₃	1	3	yes	—
7	#14579331	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
9	#14274262	C₃×C₄	1	3	yes	complemented
10	C₃×#5997⋊C₃	—	13	1	no	maximal, Hall
11	C₃×#10587721	—	14	4	no	—
12	C₁₃×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
13	C₃×#64424	—	13	1	no	—
14	C₃×#63271	—	14	4	no	—
15	C₇²×C₁₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
16	C₃×#5997	—	39	1	no	—
17	#5997⋊C₃	—	13	3	no	—
18	C₃×C₁₃×D₇	—	42	4	no	—
19	#10587721	—	14	12	no	—
20	C₃×Dic₁₃⋊C₃	—	49	1	no	maximal, Hall
21	C₃×#3861	—	13	1	no	Hall
22	C₃×C₇⋊D₇	D₁₃⋊C₃	1	1	yes	characteristic
23	#64424	—	13	3	no	—
24	C₃×C₇×C₁₃	—	2	4	no	—
25	#63271	—	14	12	no	—
26	C₂×C₃×C₁₃⋊C₃	—	49	1	no	—
27	#5997	—	39	1	no	Hall
28	C₁₃×D₇	—	42	4	no	—
29	C₃×Dic₁₃	—	147	1	no	—
30	Dic₁₃⋊C₃	—	49	3	no	—
31	C₃×C₇²	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented
32	#3861	—	13	3	no	—
33	C₃×AGL(1,𝔽₇)	—	182	4	no	—
34	C₃×C₁₃⋊C₃	—	49	1	no	Hall
35	C₇⋊D₇	C₃×D₁₃⋊C₃	1	1	yes	characteristic
36	C₇×C₁₃	—	2	4	no	—
37	C₂×C₃×C₁₃	—	147	1	no	—
38	C₂×C₁₃⋊C₃	—	49	3	no	—
39	C₃×ΓL(1,𝔽₈)	—	182	4	no	—
40	Dic₁₃	—	147	1	no	Hall
41	C₇²	C₃×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₃×D₇	—	42	4	no	—
43	AGL(1,𝔽₇)	—	182	12	no	—
44	C₃×C₁₃	#5997⋊C₃	1	1	yes	characteristic, complemented
45	C₁₃⋊C₃	—	49	3	no	—
46	C₃²×C₄	—	637	1	no	Hall
47	C₂×C₁₃	—	147	1	no	—
48	C₃×C₇	—	2	4	no	—
49	ΓL(1,𝔽₈)	—	182	12	no	—
50	C₂×C₃²	—	637	1	no	—
51	D₇	—	42	4	no	—
52	C₁₃	C₃×#5997⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₃×C₄	—	1911	1	no	—
54	C₃×C₄	—	637	3	no	—
55	C₃²	—	637	1	no	Sylow
56	C₇	—	2	4	no	—
57	C₂×C₃	—	637	3	no	—
58	C₂×C₃	—	147	1	no	—
59	C₄	—	1911	1	no	Sylow
60	C₃	—	637	3	no	—
61	C₃	#21439680	1	1	yes	characteristic, direct product factor
62	C₂	—	147	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#21439680
commutator, hypocenter	C₇²×C₁₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₃×C₄
prime radical	C₃×#16838449	C₂
cosocle	C₁₃×C₇⋊D₇	C₂×C₃²
LCS	G ▷ C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃×#14579331	C₃	semidirect
3. #21439680	C₃	direct (N × H)
4. C₃×#14274262	C₄	semidirect
7. #14579331	C₃²	semidirect
8. C₃×C₇²×C₁₃	C₃×C₄	semidirect
9. #14274262	C₃×C₄	semidirect
15. C₇²×C₁₃	C₃²×C₄	semidirect
31. C₃×C₇²	Dic₁₃⋊C₃	semidirect
41. C₇²	C₃×Dic₁₃⋊C₃	semidirect
44. C₃×C₁₃	#5997⋊C₃	semidirect
52. C₁₃	C₃×#5997⋊C₃	semidirect
61. C₃	#21439680	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#16838449	2
C₃×#14579331	3
#21439680	3
C₃×#5997⋊C₃	13
C₃×Dic₁₃⋊C₃	49

Subgroups — C3×#21439680 #37525035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21439680 #37525035